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Consider a CPU has 8 general-purpose registers
R0, R1..., R7 and supports the following operations.
ADD Ra, Rb, Rc Add Ra to Rb and store the result to Rc.
MUL Ra, Rb, Rc Multiply Ra to Rb and store the result to Rc.
An operation normally takes one clock cycles, an operation takes two clock cycles if it produces a result required by the immediately following operations. Consider the expression XY + XYZ + YZ, where variables X, Y and Z are initially located in the registers R0, R1 and R2. If contents these registers must not be modified, what is the minimum number of clock cycles required for an operation sequence that computes the value of XY + XYZ + YZ?
  • a)
    4
  • b)
    5
  • c)
    6
  • d)
    7
Correct answer is option 'C'. Can you explain this answer?
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Introduction:
In this problem, we need to compute the value of the expression XY XYZ YZ using the given CPU operations and registers. We are required to find the minimum number of clock cycles required to compute the expression without modifying the contents of the registers.

Given:
CPU has 8 general-purpose registers R0, R1..., R7.
Supported operations:
- ADD Ra, Rb, Rc: Add Ra to Rb and store the result in Rc.
- MUL Ra, Rb, Rc: Multiply Ra to Rb and store the result in Rc.
- Operation takes 1 clock cycle, but 2 clock cycles if the result is needed by immediately following operations.
Variables X, Y, and Z are initially located in registers R0, R1, and R2.

Calculating the expression:
To compute the value of the expression XY XYZ YZ, we can break it down into smaller steps:

1. Compute XY and store the result in register R3:
- MUL R0, R1, R3

2. Compute XYZ and store the result in register R4:
- MUL R3, R2, R4

3. Compute YZ and store the result in register R5:
- MUL R1, R2, R5

4. Compute the final result XY XYZ YZ and store it in register R6:
- ADD R3, R4, R6
- ADD R6, R5, R6

Calculating the minimum number of clock cycles:
To determine the minimum number of clock cycles required, we need to consider the dependencies between operations.

- Computing XY takes 1 clock cycle.
- Computing XYZ depends on the result of XY, so it takes 2 clock cycles.
- Computing YZ depends on the result of XY, so it also takes 2 clock cycles.
- Computing the final result depends on the results of XYZ and YZ, so it takes 2 clock cycles.

Therefore, the minimum number of clock cycles required for the operation sequence is 1 + 2 + 2 + 2 = 7 clock cycles.

Conclusion:
The minimum number of clock cycles required to compute the value of the expression XY XYZ YZ without modifying the contents of the registers is 7 clock cycles.
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Consider a CPU has 8 general-purpose registersR0, R1..., R7 and supports the following operations.ADD Ra, Rb, Rc Add Ra to Rb and store the result to Rc.MUL Ra, Rb, Rc Multiply Ra to Rb and store the result to Rc.An operation normally takes one clock cycles, an operation takes two clock cycles if it produces a result required by the immediately following operations. Consider the expression XY + XYZ + YZ, where variables X, Y and Z are initially located in the registers R0, R1 and R2. If contents these registers must not be modified, what is the minimum number of clock cycles required for an operation sequence that computes the value of XY + XYZ + YZ?a)4b)5c)6d)7Correct answer is option 'C'. Can you explain this answer?
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